Asymptotics of the KPP minimal speed within large drift

TL;DR

This paper investigates how the minimal KPP speed of reaction-advection-diffusion equations behaves asymptotically as the drift magnitude becomes very large, providing explicit limits and conditions for different dimensions.

Contribution

It establishes the limit of the minimal KPP speed as drift tends to infinity and characterizes the conditions under which the speed scales linearly with the drift magnitude.

Findings

The minimal KPP speed converges to a specific limit as drift M approaches infinity.

A necessary and sufficient condition is identified for the speed to grow linearly with M.

The results hold in any space dimension N.

Abstract

This Note is concerned with the asymptotic behavior of the minimal KPP speed of propagation for reaction- advection-diffusion equations with a large drift Mq (where q is the advection). We first give the limit of the speed as M\rightarrow+\infty in any space dimension N. Then, we give the necessary and sufficient condition that the advection field should satisfy so that the speed acts as O(M) as M \rightarrow+\infty.